NASA Technical Reports Server (NTRS) 20050060915: Input Files and Procedures for Analysis of SMA Hybrid Composite Beams in MSC.Nastran and ABAQUS

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by  NASA Technical Reports Server (NTRS)

NASA/TM-2005-213517
Input Files and Procedures for Analysis of SMA
Hybrid Composite Beams in MSC.Nastran and
ABAQUS
Travis L. Turner
Langley Research Center, Hampton, Virginia
Hemant D. Patel
MSC.Software Corporation, Santa Ana, California
January 2005
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NASA/TM-2005-213517
Input Files and Procedures for Analysis of SMA
Hybrid Composite Beams in MSC.Nastran and
ABAQUS
Travis L. Turner
Langley Research Center, Hampton, Virginia
Hemant D. Patel
MSC.Software Corporation, Santa Ana, California
National Aeronautics and
Space Administration
Langley Research Center
Hampton, Virginia 23681-2199
January 2005
Acknowledgments
The first author gratefully acknowledges assistance from Adam Przekop (National Institute of
Aerospace, Hampton, VA) in generating the Python scripts for data extraction from the ABAQUS output
database files.
Available from:
NASA Center for AeroSpace Information (CASI) National Technical Information Service (NTIS)
7121 Standard Drive 5285 Port Royal Road
Hanover, MD 21076-1320 Springfield, VA 22161-2171
[phone] [phone]
Abstract

A thermoelastic constitutive model for shape memory alloys (SMAs) and
SMA hybrid composites (SMAHCs) was recently implemented in the
commercial codes MSC.Nastran and ABAQUS. The model is implemented
and supported within the core of the commercial codes, so no user
subroutines or external calculations are necessary. The model and resulting
structural analysis has been previously demonstrated and experimentally
verified for thermoelastic, vibration and acoustic, and structural shape
control applications. The commercial implementations are described in
related documents cited in the references, where various results are also
shown that validate the commercial implementations relative to a research
code. This paper is a companion to those documents in that it provides
additional detail on the actual input files and solution procedures and serves
as a repository for ASCII text versions of the input files necessary for
duplication of the available results.

Introduction

Shape memory alloys (SMAs) are being considered for an ever-increasing number and variety of
applications. While practical knowledge of SMAs has increased significantly in recent years, no practical
modeling tool has been made available to engineers and researchers. Furthermore, SMA hybrid
composite (SMAHC) structures, conventional composite structures with embedded SMA actuators, are
receiving significant interest. SMAHC structures present even greater numerical modeling difficulties
because of the complex interactions between the constituents.

A thermoelastic constitutive model for such SMAHC material systems and structures was previously
developed by Turner.1 This model is based upon definition of a nonlinear, effective coefficient of thermal
expansion (CTE) and is relatively intuitive, simple to use, and requires only fundamental engineering
properties of the constituent materials. A research finite element (FE) code was developed around this
constitutive model. The research code has been used for numerical studies and for experimental
validation of the model.2-5 The model was recently implemented in the commercial finite element codes
MSC.Nastran and ABAQUS, as reported by Turner and Patel.6-7 The model is supported within the core
of current releases of both codes, so no user subroutines or external calculations during solution are
necessary. Details of the theory behind the model are presented in reference 1. An overview of the
manner in which the model can be used in the commercial codes is given in references 6 and 7, followed
by results for thermal post-buckling and random vibration control of clamped SMAHC beams and
deflection control of cantilevered SMAHC beams. The results show excellent agreement between the
commercial codes and the research code in all cases. A web link is cited in references 6 and 7 (and
below) that provides all of the input files necessary to duplicate the results presented in those papers.

The objectives of this paper are to describe the specific input files in more detail than is possible in the
other publications, describe the solution processes in more detail, and serve as a repository for ASCII
listings of all of the files necessary to regenerate the results in references 6 and 7. It is hoped that the
information in references 6 and 7, the additional detail in this publication, and the input files in electronic
or text form (in this document) will enable the reader to rapidly understand the usage of the model in
MSC.Nastran and ABAQUS and enable adaptation of these methods to a wide variety of research and
industrial applications.

1
General Comments

The input files necessary to regenerate the results in references 6 and 7 are available online at
http://stabserv.larc.nasa.gov. There are three subfolders in this distribution including
“deflection_control,” “post-buckling,” and “random_vibration.” The subfolder names indicate their
respective content necessary to duplicate the deflection control, thermal post-buckling, and random
vibration results from references 6 and 7. In the event that these files are ever unavailable, they are
presented in ASCII text form in Appendices A–F. The remainder of this section is dedicated to general
comments on the files in the distribution. Some filename suffix definitions are as follows.
*.bdf MSC.Nastran analysis input file (bulk data file)
*.dat Material property data file, ABAQUS data file (ASCII), or results comparison data file
*.fil ABAQUS results file (binary)
*.f06 MSC.Nastran output file (ASCII)
*.inp ABAQUS analysis input file
*.odb ABAQUS output database file (binary)
*.pch MSC.Nastran punch file (ASCII)
*.py ABAQUS Python script
Two beam configurations are considered in this study including a 18×1 inch beam clamped at both ends
and a 9×1 inch cantilever beam. Two SMAHC laminates are analyzed for each beam configuration. The
SMAHC laminates include one having single wide ribbon Nitinol inclusions along the centerline of the
beam in specific layers and the other having uniformly distributed Nitinol inclusion over the extent of
specific layers. Schematics of a representative beam cross section for the two laminates are shown in
Figure 1a and b, where unrealistically few layers are shown for clarity.

SMA/ SMA/
Host Host
Host Host
((aa)) ((bb))

Figure 1: Representative beam cross sections for the mon (a) and mix0 (b) SMAHC laminate types.
The FE mesh used in this study has 4 elements across the width of the beam cross sections. Application
of the mesh to the laminate in Figure 1a results in the outer two rows of elements consisting of host
material only and the inner elements have layers that alternate between 100% Nitinol (monolithic Nitinol
inclusion) and 100% host composite. In contrast, the same FE mesh applied to the laminate in Figure 1b
results in identical lamination for all elements with layers consisting of host composite only or mixtures
of Nitinol and host composite (mixture Nitinol inclusion with 0° orientation). These laminates will be
referred to as mon and mix0 SMAHC laminate types, indicating the respective monolithic and mixture
Nitinol content in representative finite element cross sections. The mon laminates considered in this study
have differing glass-epoxy and Nitinol layer thicknesses of 0.004875 and 0.006 inches, respectively.
Thus, the necessary material properties for elements of the mon laminate type include those to
characterize the constituents alone and the resulting two element types (glass-epoxy only and SMAHC)
have differing thickness but the same mid-plane. Elements of the mix0 laminate type require material
properties to characterize the host material alone and in combination with Nitinol. Also, all layers have
the same thickness (0.004875 inches) for the mix0 laminates analyzed in this study. These two attributes
result in uniform element thickness and properties for elements of the mix0 laminate type. The
MSC.Nastran and ABAQUS input files associated with the two material types are distinct, as indicated by
the presence of the string “mix0” in the root of the file name for analyses involving the SMAHC
laminates with the mixture layers (mix0 laminates). The material property data files have the following
naming convention.
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materialcode_1dir2dir75.dat
• material – glep, niti, or smahcmix0 indicating that the material property data is representative of glass-
epoxy, Nitinol, or of a SMAHC mixture layer with Nitinol in the 0° direction, respectively.
• code – nast or abaq indicating that the material property data is in a format consistent with
MSC.Nastran or ABAQUS input, respectively.
• 1dir and 2dir – sec, tan, or stn indicating that the thermal expansion data in the material property data
file is secant CTE values, tangent CTE values, or thermal strain values, respectively. The data type
indication is given for both the 1 and 2 principal material coordinate directions.
• 75 – indicates that the material property data is specific to a reference temperature of 75°F.

The properties given for the SMAHC mixture (smahcmix0) were evaluated using the relations for
effective material properties in Equations (7) of references 6 and 7. Note that the native form for the
thermal expansion properties of Nitinol is thermal strain in the 1-direction and tangent CTE in the 2-
direction. That for glass-epoxy is tangent CTE in both the 1- and 2-directions. These native forms are
dictated by the corresponding experimental measurement(s) and subsequent data processing. Thermal
strain for Nitinol in the 2-direction was calculated by integrating the tangent CTE values. Secant CTEs
for Nitinol were calculated from the corresponding thermal strain values. Similarly, thermal strain values
for glass-epoxy were calculated by integrating the tangent CTE data and secant CTE values were
subsequently calculated from the thermal strain data.

The root names of the MSC.Nastran analysis input files end with “_n” or “_in” and the root names of the
ABAQUS analysis input files end with “_a”. This was done because the two commercial codes
automatically generate several auxiliary files during each run and this distinction avoids the potential for
the two codes to write to the same auxiliary file name. The distinction between the “_n” and “_in” root
names for the MSC.Nastran analyses is explained below. The ASCII text versions of the input and
associated data files have the following organization in the appendices.
• Appendices A, C, E – MSC.Nastran analysis input files, FE mesh “include” files, and material property
“include” files, respectively
• Appendices B, D, F – ABAQUS analysis input files, FE mesh “include” files, and material property
“include” files, respectively
The following sections further describe the files and procedures associated with performing thermal post-
buckling, linear random response, and deflection control simulations of the SMAHC beams. Specific file
names associated with the example problems are indicated in bold type.

Thermal Post-Buckling Control

The files associated with thermal post-buckling analysis of SMAHC beams are contained in the folder
“post-buckling.” The beams have a length and width of 18×1 inches with clamped boundary conditions
at both ends and a spatially uniform temperature of 250°F is taken as the thermal load. The lamination
stacking sequence is (45/0/-45/90) with the Nitinol actuators in the 0° layers, giving an overall thickness
2s
of 0.0825 and 0.078 inches for the mon and mix0 laminates, respectively. All of the analysis input files
have “include” statements to incorporate the common files specifying the nodal coordinates, element
connectivity, and material properties. The nonlinear static solutions in both commercial codes require
some “perturbation” to avoid convergence on the trivial solution. This requirement is accommodated in
these analyses by first performing a static solution under gravity load and using the resulting deflections
as geometric imperfections in the thermal post-buckling analyses. Descriptions of the solution process in
each of the commercial codes are given in the following subsections.

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MSC.Nastran Analysis

The MSC.Nastran input files associated with the gravity load analyses for the mon and mix0 laminates are
smahcbeamg_n.bdf and smahcbeammix0g_n.bdf, respectively. Note that smahcbeamg_n.bdf uses the
unperturbed nodal coordinates in nodes.bdf and element properties associated with the mon laminate,
which consists of glass-epoxy elements in the outer rows (glep_outer_elem.bdf) and SMAHC elements
in the inner rows (smahc_inner_elem.bdf). The element properties for the mon laminate are determined
from the independent constituent properties in glepnast_secsec75.dat and nitinast_secsec75.dat. The
mix0 laminate found in smahcbeammix0g_n.bdf also uses the unperturbed nodal coordinates in
nodes.bdf and has uniform properties for all elements in smahc_all_elem.bdf, as defined by
glepnast_secsec75.dat and smahcmix0nast_secsec75.dat. The gravity deflections from the
MSC.Nastran runs were extracted from the output files smahcbeamg_n.f06 and
smahcbeammix0g_n.f06 and used to perturb the nodal coordinates in nodes.bdf to create the
“imperfect” geometry represented in nodes_imon.bdf and nodes_imix0.bdf, respectively. There are
many ways in which the gravity deflection data might be extracted from the “f06” files and used to alter
the nodal coordinates. The provided utility bdf_node_alter.f was used in the present work. The gravity
analysis input and supporting files are summarized as follows.
• smahcbeamg_n.bdf – gravity load analysis for mon laminate case
o nodal coordinates: nodes.bdf
o element properties and connectivity: glep_outer_elem.bdf, smahc_inner_elem.bdf
o material properties: glepnast_secsec75.dat, nitinast_secsec75.dat
• smahcbeammix0g_n.bdf – gravity load analysis for mix0 laminate case
o nodal coordinates: nodes.bdf
o element properties and connectivity: smahc_all_elem.bdf
o material properties: glepnast_secsec75.dat, smahcmix0nast_secsec75.dat
• bdf_node_alter.f – utility to alter unperturbed nodal coordinates with gravity deflections
o mon laminate case
(cid:131) input files: smahcbeamg_n.f06 and nodes.bdf
(cid:131) output file: nodes_imon.bdf
o mix0 laminate case
(cid:131) input files: smahcbeammix0g_n.f06 and nodes.bdf
(cid:131) output file: nodes_imix0.bdf

The thermal post-buckling input files for the mon laminate case are smahcbeamr_in.bdf,
smahcbeams_in.bdf, and smahcbeamt_in.bdf. The three input files are identical except for the manner
in which thermal expansion data is included in the model. Tangent CTE data is used for glass-epoxy and
a combination of thermal strain and tangent CTE data is used for Nitinol in smahcbeamr_in.bdf;
“included” from glepnast_tantan75.dat and nitinast_stntan75.dat. Thermal strain data is used for both
glass-epoxy and Nitinol in smahcbeams_in.bdf; “included” from glepnast_stnstn75.dat and
nitinast_stnstn75.dat. Finally, secant CTE data is used for both glass-epoxy and Nitinol in
smahcbeamt_in.bdf; “included” from glepnast_secsec75.dat and nitinast_secsec75.dat. A similar
description applies for the mix0 laminate case input files smahcbeammix0r_in.bdf,
smahcbeammix0s_in.bdf, and smahcbeammix0t_in.bdf. Note that all of the thermal post-buckling
input files require geometric imperfections, which are provided by incorporation of the nodal coordinates
in nodes_imon.bdf and nodes_imix0.bdf for the mon and mix0 laminate cases, respectively. Also, note
that this is the source for the distinction between the MSC.Nastran analysis input file root names ending
in “_n” and “_in”, meaning the absence and presence of geometric imperfections, respectively. For cases
when imperfections are required for the analysis, the “_n” input files are included for reference only. The
thermal post-buckling input and supporting files for the mon laminate case are summarized as follows.

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• smahcbeamr_in.bdf – thermal post-buckling analysis with tangent CTE/thermal strain data
o nodal coordinates: nodes_imon.bdf
o element properties and connectivity: glep_outer_elem.bdf, smahc_inner_elem.bdf
o material properties: glepnast_tantan75.dat, nitinast_stntan75.dat
• smahcbeams_in.bdf – thermal post-buckling analysis with all thermal strain data
o nodal coordinates: nodes_imon.bdf
o element properties and connectivity: glep_outer_elem.bdf, smahc_inner_elem.bdf
o material properties: glepnast_stnstn75.dat, nitinast_stnstn75.dat
• smahcbeamt_in.bdf – thermal post-buckling analysis with all secant CTE data
o nodal coordinates: nodes_imon.bdf
o element properties and connectivity: glep_outer_elem.bdf, smahc_inner_elem.bdf
o material properties: glepnast_secsec75.dat, nitinast_secsec75.dat
The corresponding summary for the mix0 laminate case follows similarly.
• smahcbeammix0r_in.bdf – thermal post-buckling analysis w/ tangent CTE/thermal strain data
o nodal coordinates: nodes_imix0.bdf
o element properties and connectivity: smahc_all_elem.bdf
o material properties: glepnast_tantan75.dat, smahcmix0nast_stntan75.dat
• smahcbeammix0s_in.bdf – thermal post-buckling analysis with all thermal strain data
o nodal coordinates: nodes_imix0.bdf
o element properties and connectivity: smahc_all_elem.bdf
o material properties: glepnast_stnstn75.dat, smahcmix0nast_stnstn75.dat
• smahcbeammix0t_in.bdf – thermal post-buckling analysis with all secant CTE data
o nodal coordinates: nodes_imix0.bdf
o element properties and connectivity: smahc_all_elem.bdf
o material properties: glepnast_secsec75.dat, smahcmix0nast_secsec75.dat

MSC.Nastran “punch” files of mid-span deflection versus load factor are requested in each thermal post-
buckling input file. The resulting punch files were read into Microsoft Excel. Equations were introduced
to normalize the load factor to temperature (i.e., 0–1 → 75°F–150°F and 1–2 → 150°F–250°F) and to add
the initial imperfection (mid-span gravity deflection from smahcbeamg_n.f06 or
smahcbeammix0g_n.f06) to the thermal post-buckling deflection. The results of this process are
contained in the files smahcbeam_in.xls and smahcbeammix0_in.xls.

ABAQUS Analysis

The ABAQUS input files associated with the gravity load analyses for the mon and mix0 laminate cases
are smahcbeamg_a.inp and smahcbeammix0g_a.inp, respectively. Analogously to the MSC.Nastran
analyses, these input files make use of the unperturbed nodal coordinates in nodes.inp and the
corresponding material and element property definitions. The gravity analysis input and supporting files
are summarized as follows.
• smahcbeamg_a.inp – gravity load analysis for mon laminate case
o nodal coordinates: nodes.inp
o element properties and connectivity: glep_outer_elem.inp, smahc_inner_elem.inp
o material properties: glepabaq_secsec75.dat, nitiabaq_secsec75.dat
• smahcbeammix0g_a.inp – gravity load analysis for mix0 laminate case
o nodal coordinates: nodes.inp
o element properties and connectivity: smahc_all_elem.inp
o material properties: glepabaq_secsec75.dat, smahcmix0abaq_secsec75.dat

5
The “results files” from the ABAQUS gravity load analyses (i.e., smahcbeamg_a.fil and
smahcbeammix0g_a.fil) are used directly as geometric imperfection input using the *IMPERFECTION
option in the corresponding post-buckling analyses smahcbeamt_a.inp and smahcbeammix0t_a.inp,
respectively. The thermal post-buckling analysis input and supporting files are summarized as follows.
• smahcbeamt_a.inp – thermal post-buckling analysis for mon laminate case
o nodal coordinates: nodes.inp
o geometric imperfections: smahcbeamg_a.fil
o element properties and connectivity: glep_outer_elem.inp, smahc_inner_elem.inp
o material properties: glepabaq_secsec75.dat, nitiabaq_secsec75.dat
• smahcbeammix0t_a.inp – thermal post-buckling analysis for mix0 laminate case
o nodal coordinates: nodes.inp
o geometric imperfections: smahcbeammix0g_a.fil
o element properties and connectivity: smahc_all_elem.inp
o material properties: glepabaq_secsec75.dat, smahcmix0abaq_secsec75.dat
Note that thermal post-buckling analysis in ABAQUS is performed using secant CTE data only. Analysis
in ABAQUS is also possible with thermal strain data by employing the USER parameter on the
*EXPANSION option and defining the user subroutine UEXPAN, but this is not explored in this study.
Analysis in ABAQUS is not possible using tangent CTE values.

The Python scripts smahcbeamt_a.py and smahcbeammix0t_a.py extract the output from the thermal
post-buckling output databases smahcbeamt_a.odb and smahcbeammix0t_a.odb, respectively. The
scripts extract mid-span displacement versus “time” from the output databases, normalize time to
temperature (i.e., 0–1 → 75°F–150°F and 1–2 → 150°F–250°F), add the initial imperfection (gravity
deflection from smahcbeamg_a.dat or smahcbeammix0g_a.dat) at the mid-span to the thermal post-
buckling deflection, and to write results to smahcbeamt_a.wvt and smahcbeammix0t_a.wvt,
respectively. The scripts are run via the command “abaqus python ‘script name’.”

The mid-span deflection versus temperature data from all MSC.Nastran and ABAQUS post-buckling
analyses, as well as the results from the research code, were compiled for the mon and mix0 laminate
beams in the ASCII data files (formatted for Tecplot) smahcbeam_wvtcmp.dat and
smahcbeammix0_wvtcmp.dat, respectively. These data were used to generate the plots of mid-span
deflection versus temperature in references 6 and 7.

Random Vibration Control

The files necessary for simulation of the random vibration response of SMAHC beams are in the folder
“random_vibration.” The beam model of the previous section is used, i.e., 18×1 inch beam clamped at
both ends and subjected to a uniform thermal load of 250°F, but only the mon laminate case and only the
secant CTE thermal expansion data are considered in this part of the study. The excitation is taken to be
band-limited white noise inertial load (base acceleration) with a bandwidth of 0–400 Hz and a RMS value
of 0.25g. This RMS load corresponds to a spectral level of approximately 23.32 (in/s2)2/Hz. The modal
approach is used in all dynamic analyses incorporating the first 10 modes and a uniform critical damping
ratio of 0.5% for all modes. All of the analysis input files have “include” statements to incorporate the
common files specifying the nodal coordinates, element connectivity, and material properties. The intent
of these random vibration analyses is to examine the dynamic response of the beams at various
thermoelastic equilibrium states throughout the thermal post-buckling range, the solution to which was
described in the Thermal Post-Buckling Response section. Thus, the thermal post-buckling solutions
must be performed prior to or in series with the dynamic solutions.

6